Development of a model of the useful effect of the system at different levels of subsystem interchangeability in the problem of optimizing the allocation of a limited resource

Abstract

The object of this study is the process of optimizing the allocation of limited resources among the subsystems of a large complex system. The problem addressed lies in the insufficient adequacy of existing utility models, which fail to account for the degree of subsystem interchangeability and therefore cannot accurately predict optimal resource distribution. The core result is the development of a universal utility model based on logistic dependencies and a flexible scalar convolution constructed using a modified marginal Kolmogorov-Gabor polynomial with the coefficient kAdd, which governs interchangeability. Complete trajectories of optimal solutions were obtained for various values of total resources and interchangeability levels. It was found that variations in these parameters alter the optimal effect by 25–35% under conditions of significant resource scarcity. The problem was resolved by combining the universality of logistic models with the flexibility of the new convolution, which generalizes additive, multiplicative, and minimizing forms and enables continuous adjustment of the model to reflect subsystem interaction characteristics. The observed patterns indicate that at low interchangeability, resources are distributed more evenly, while at high interchangeability, they are concentrated in the most efficient subsystem, significantly enhancing the overall effect under resource deficit conditions. The results are applicable to the design and management of large complex systems – such as IT security, crisis management, and organizational design – where informed decisions are required regarding the allocation of limited resources while considering structural flexibility. This approach is particularly suitable when statistical data are available for calibrating the logistic parameters of subsystems and assessing their interchangeability.